SoI don't have to explain classical information to you anymore.
But quantum information is mysterious.
And you often find yourself.
What is it?"
AndI start telling them about Hilbert space,
andso on like that.
And they get plays over there, not very interested.
SoI have to find a way of explaining it.
And the best way I can think of is to say that
quantum information is like the information in the dream.
If you try to describe your dream to someone else,
And you only remember what you said about it. And you can't prove tosomeone what you dreamed.
And you can lie about your dream and not get caught,
except maybe if you try to lie to your spouse about your dream.
Well, anyway, but unlike dreams,
despite the best efforts of Sigmund Freud,
there is a well-understood theory about how quantum information behaves.
And that's what I want to talk about today.
The basic principle of quantum mechanics and of quantum information is that
in any physical system, there is a maximum number of reliablydistinguishable states.
And for very simple system like these polarized photons, we've beentalking about,
there are two reliably distinguishable states.
And that between any pair of reliably distinguish states,
there are other intermediate states
that are not just reliably distinguishable from either of those.
Now, it doesn't mean that only some states are reliably distinguishable.
If any pair of states,
the possible physical states correspond to directions in space,
not ordinary three dimensional space.
But inner space with as many dimensions as
the system’s maximum number of reliably distinguishable states.
So for a photon, that's two.
And if the directions are perpendicular, then the states are distinguishable.
If they're not perpendicular, they are not distinguishable by any procedure at all.
So that's it. In a nutshell, that's quantummechanics.
So that's not so hard to understand.
So let's look at some of the manifestations of that.
But before saying that, this is something physicists have understood,
but they hadn't thought of it as having to do with information.
Now we know that ordinary information is reducible to bits,
We can take anything, however complicated, digitize it,
and produce it to a lot of zeros and ones.
And all processing of it can be reduced to
acting on these zeros and ones with ANDs and NOTs.
And that if you make the bits smaller andfaster and cheaper,
you just make the computer more and more useful.
It doesn't matter what you used to carry the bits.
If you have something that can you dozeros andones
and ANDs and NOTs, you're good to go.
Now,physicists haven't thought this way.
But you can make the analogous statements about quantum information.
Quantum information reducible to qubits
that is any kind of two-state system, such as a polarizedphoton.
And any processing of it,
any manipulation of a quantum state can be reduced to actions
on those one and two at a time.
That was only really discovered in about 1995.
And just as classical bits, can become independent of their physical embodiment
for their mathematical uses or for the uses of communication.
Soqubits and quantum gates are
fungibleamong the different quantum systems.
So here’s the example that you've seen this kind of diagram before.
But, so we know that we can use a single polarized photon to carry a bit of information.
If we set it up like this, the horizontal photons will go straight through(crystal).
The vertical photons will be deviated
and can count them on two separate counters.
But if you put in diagonal photons,
instead of being deviated by an intermediate amount,
they will some of them go into the this beam
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